As shown in FIGS. 1-4, a children's bicycle 10 of the prior art has a chain ring shaft tube 11 which is provided at both ends thereof with a position confining recess 12. The bicycle 10 also has an axle 13 which is provided at both ends thereof with a crank arm 15 having a shaft support hole 14. A chain ring 16 is mounted on the axle 13, which is fastened pivotally to the shaft tube 11 by two shaft support members 17 and 18, which comprise an annular tube member 20 having an annular lip 21, an insertion protrusion 22, an annular cell 23, a stepped annular edge 24, and a semiannular plate member 26 having a stop edge 25. The shaft support member 18 is further provided with a fine annular plate 27, a wide annular plate 28, and an elastic annular member 29. A tubular bolt member 30 is received in a support hole 31 of the axle 13. The prior art axle pivoting structure is too complicated and can not be easily assembled.